Question

A gas laser has a cavity length of 1/3 m and a single oscillation frequency of 9.0 x 1014 Hz. What is the cavity mode number?

Answer 1

2 × 10⁶

Step-by-step explanation:

Data provided in the question:

Cavity length, L =
`(1)/(3)m`

Oscillation frequency,
`f_m` = 9.0 × 10¹⁴ Hz

Now,

we know,

`f_m=(c)/(\lambda_m)`

here,

c is the speed of light = 3 × 10⁸ m/s

`\lambda_m` = Wavelength of mode m inside the laser cavity

m is the cavity mode number

Thus,

`9.0*10^(14)=(3*10^8)/(\lambda_m)`

or

`\lambda_m` =
`(1)/(3)` × 10⁻⁶

Also,

`m\lambda_m = 2L`

Therefore,

m ×
`(1)/(3)` × 10⁻⁶ = 2 ×
`(1)/(3)`

or

m = 2 × 10⁶